Aircraft: LANCAIR EVOLUTION
Phase of flight: Descent; Cruise
Anomaly: ATC Issue All Types; Aircraft Equipment Problem Critical; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence

The plane had been at ZZZ for the previous two days for maintenance (replaced batteries; adjusted landing gear and landing gear warning system; and performed 411 and 413 IFR certifications). I departed ZZZ at about XA:30 local. There were rain showers in the area with patchy cloudy conditions and some localized thunderstorms and cumulus clouds. Expected conditions at the time of landing at my destination ZZZ1 were clear with light winds. This was my first night flight in the airplane but I felt comfortable flying the plane - departing in daylight and landing in clear night conditions. I consulted with my instructor prior to departure and he confirmed he felt the flight was manageable.Flight plan was filed for 23;000 ft. Climbout was normal through several cloud layers and deviations right of course to avoid thunderstorms. Some IFR; but mostly VFR between clouds and layers up to 23;000 ft. Pitot heat was turned on shortly after departure.It was getting dusk as I leveled off. I could see a stratus deck of clouds ahead at what appeared to be between 23;000 ft [and] 24;000 ft. I requested an altitude change to 25;000 ft which was immediately granted. My interior windows began to fog up and became coated with light ice. I turned on the defrost; but the fog and ice were growing and defrost didn't seem to do much good. Upon leveling at 25;000 ft in clear air I began to wipe down the interior windscreen with a towel to remove the fog and ice. I noticed my airspeed became erratic and then began to drop. I suspected ice in the pitot / static system. I confirmed the pitot heat was on. I assumed I was picking up ice. I could not visually detect any ice on the wings; but it was difficult to see because of the interior fogged and iced windows. When I wiped the interior of the windscreen it did not show any ice on the outside of the windscreen. Nevertheless; I turned on the de-ice; propeller heat; initial separator; and alternator (as discussed earlier that afternoon with mechanics as the proper procedure). By now it was mostly dark.My location was about 15 miles south of ZZZZZ heading direct to ZZZ1. The AOA (Angle of Attack indicator) began blaring loudly 'PUSH; PUSH' as my indicated airspeed dropped. The loud blaring 'PUSH' was constant and so distracting; it was hard to concentrate on anything else. I believed the problem was ice blocking the pitot / static system and that perhaps my pitot heat was not working; and; although I couldn't detect any exterior ice; perhaps some ice had accumulated thereby slowing my airspeed. I requested a lower altitude of 17;000 ft thinking that a lower altitude with warmer temperatures would help when combined with the de-ice systems I had turned on a few minutes earlier.Center was talking to me about a new altitude and heading but it was very hard to hear with the blaring AOA. The autopilot would not work with the indicated airspeed and my altitude began to fluctuate. I explained to Center I was having instrument problems and requested delaying vectors to sort out the issues. I couldn't hear most of what Center was saying; but attempted straight and level flight by hand as I evaluated the situation. Center approved delayed maneuvering in my current area.In the dark it took some time to find the AOA circuit breaker; which I pulled and the blaring 'PUSH; PUSH' finally stopped. At some point my instruments seemed to become more stable and reliable so I requested to resume flight to my destination but at a lower altitude of 17;000 ft thinking the ice issue had been resolved. However; quickly I realized the problems were not resolved and I requested a return to ZZZ. I [requested priority handling] with Center. They cleared me back to ZZZ. Soon; Center switched me over to Approach. I repeated my [priority request] and requested vectors to ZZZ.I realized my backup L3 instrument was giving me the same airspeed and altitude readings as the PFD so it was not useful. I erroneously believed the altitude indicator was working; but knew the airspeed was not reliable. I repeatedly asked Center and then Approach to confirm my altitude. In each instance they confirmed my altitude as being the same as shown on my altimeter. Flying back to ZZZ; Approach began giving me lower altitudes. As I pushed the nose over I had the distinct sense of descending but the altimeter either did not move or moved erratically. After several queries to Approach about my altitude; they asked me if I was suffering from vertigo. I'm not sure I could diagnose it under the circumstance; but I said no.The night was dark with overhead clouds and no ground references. At some point heading back to the ZZZ2 area and flying by hand since the autopilot would not work given the erratic instrument readings; I moved my attention to the cockpit trying to continue to trouble shoot and diagnose the problems. When I looked back at my heading indicator I realized I was turning in a spiraling descent. I quickly leveled the wings and corrected my flight path but it reminded me how easy it is to fall into a death spiral without any visual references.As I approached ZZZ3; Approach said I needed to begin descending and advised me not to worry about the restricted area because they had asked the military to turn it cold. I said I had been trying to descend for several minutes by pushing the nose down; but other than intuition I was unsure whether I was descending because of the erratic airspeed and altitude readings. I continued to periodically ask Approach what they showed as my altitude and they continued to repeat 17;000 - 18;000 ft. Soon some ground lights came into view. As I passed over them it was clear my altitude was no more than 2;000 - 3;000 ft above the ground. I immediately stopped my descent and again asked Approach about my altitude. When the Controller said 17;000 ft. I replied that his information was wrong and that my altitude was no more than 3;000 ft. He immediately told me to climb to 4;500 ft which was the minimum vectoring altitude in the area. I initiated a climb and enabled GPS altitude on my iPad ForeFlight which confirmed I was climbing through 3;500 ft. A few moments later; Approach said he realized he was only getting my ADS-B / Transponder altitude and was just reading back to me what my instruments were telling him. The Controller had no other radar altitude available to him.About this point; I concluded; given the difficulty of flying the plane with inaccurate instruments in night mostly visual; but some IFR; conditions; that trying to proceed to ZZZ was not wise. I told Approach I wanted to divert and land at ZZZ2. They instructed me to turn north and look for the airport beacon. I immediately saw the beacon and headed for it. As I approached they cleared me to land on Runway XXL. I could hear on the radio as ATC cleared other traffic and asked an [aircraft] on final to go-around.I was unable to immediately spot the runway because of the highway and other city lights; but I had the airport on ForeFlight and turned into a left downwind at what seemed about the right distance. I set my torque at the settings I learned in training less than two weeks before to deliver the desired pattern and landing speeds. On the downwind I saw the runway; turned base and then final. Although my instruments were reading crazy numbers; the final approach was smooth and stable and on the VASI visual glidepath. Landing was uneventful. Tower told me to stop on the runway; and switch to Ground who would guide me to the FBO. When I stopped on the runway; I took a picture of my instruments - they showed airspeed of 410 kts and altitude of 13;000 ft.Fire and rescue trucks followed me as I then taxied to [company] where the plane was hangered overnight. When I climbed out of the plane; the fire and rescue personnel asked if I was okay. I replied yes; thanked them; and they then departed. In the hangar; I powered on and off the systemtwice. Both times the system gave similar reading on the instruments as I had seen stopped on the runway. I also checked the pitot tube heat. It quickly got hot when turned on. A Lancair Evolution pilot reported unreliable altitude and airspeed indications while in icing conditions and ATC echoing false readings; resulting in a diversion and CFTT before landing.